I know it will work if I add it to cheapantivirus.me zone. I want client to be able to use my subdomain with blogspot.com so instead of I manually add their subdomain to my own domain zone, I can just provide them with DNS module and they them self can add their own subdomain.cheapantivirus.me to the DNS zone.

If you have friends that have blogger account and need a free subdomain to use with blogger, you can provide them with.